Major and minor 3rds as they relate to chords

Hi Fellow Tuners,

Need some pointing in the right direction please. Where do I post a
music theory question as it relates to 12tEQ please?

I posted the following question to
http://members.boardhost.com/mtr1/index.html?1054913235
but received no reply. The forum is not that active.

Here is my question:

This has always puzzled me. Can anyone please help me understand why
for example in the key of "C" Major, the bottom interval of a C Major
triad (i.e. C, E, G) which is a major 3rd, dominates the sound of
this triad which identifies the chord as Major?

In other words, the C Major chord has a major 3rd interval from C to
E and a minor 3rd interval from E to G. Obviously, if I were to sound
this chord on a piano, both intervals would be sounded at the same
time. Why then does the bottom interval (Major 3rd , C to E)seem to
identify the overall sound of the triad a smajor?

I understand that the chord does in fact sound like a major chord but
why does the bottom interval (C to E)and not the top interval (minor
3rd, E to G)seem to control the overall sound of the chord? It seems
to dominate over the minor 3rd (E to G).

The same goes for the C minor triad (C - Eb - G). The bottom interval
is a minor 3rd (C - Eb) and the top interval is a Major 3rd (Eb - G).
Why also does the bottom Major 3rd interval (and not the top interval)
dominate the overall sound of the C minor chord?

Thank you
Walter New Jersey

on 6/6/03 7:19 PM, Walter Lepore <earth7@optonline.net> wrote:

> This has always puzzled me. Can anyone please help me understand why
> for example in the key of "C" Major, the bottom interval of a C Major
> triad (i.e. C, E, G) which is a major 3rd, dominates the sound of
> this triad which identifies the chord as Major?
>
> In other words, the C Major chord has a major 3rd interval from C to
> E and a minor 3rd interval from E to G. Obviously, if I were to sound
> this chord on a piano, both intervals would be sounded at the same
> time. Why then does the bottom interval (Major 3rd , C to E)seem to
> identify the overall sound of the triad a smajor?
>
> I understand that the chord does in fact sound like a major chord but
> why does the bottom interval (C to E)and not the top interval (minor
> 3rd, E to G)seem to control the overall sound of the chord? It seems
> to dominate over the minor 3rd (E to G).
>
> The same goes for the C minor triad (C - Eb - G). The bottom interval
> is a minor 3rd (C - Eb) and the top interval is a Major 3rd (Eb - G).
> Why also does the bottom Major 3rd interval (and not the top interval)
> dominate the overall sound of the C minor chord?
>
> Thank you
> Walter New Jersey

Chords are heard in reference to some implied fundamental tone. The
presence of the 3 tones in a major triad which are _approximately_ in the
frequency ratio 4:5:6 implies a fundamental tone, i.e. you kind of hear
1:4:5:6. In this case since 1 the same "note" as 4 but 2 octaves lower, you
can say in effect that the 4 tone is heard as the root of the chord.

Therefore the important intervals to the ear are 4:5 and 4:6, major 3rd and
major 5th. Since the 5 tone is not the base, the 5:6 ration is not primary.

This also works with inversions. If you play a C chord with G as the low
note, your triad has the relationship 3:4:5. Still this implies 1:3:4:5 and
so the implied 1 or the actually present 4 is the root of the chord.

I'm not going into all the full potential detail here, so let's see how that
sits with you, and what needs clarification. And this is just one way of
saying it, and someone else may have a clearer answer.

-Kurt Bigler

>Here is my question:
>
>This has always puzzled me. Can anyone please help me understand why
>for example in the key of "C" Major, the bottom interval of a C Major
>triad (i.e. C, E, G) which is a major 3rd, dominates the sound of
>this triad which identifies the chord as Major?

That's a good question, Walter.

Around here, we say that the consonances of equal temperament
approximate just intonation.

In just intonation, there is also a distinction between "major" and
"minor" triads. The former is usually written 4:5:6. If the bottom
tone is 100 Hz., the middle one would be 125 Hz., and the top one
150 Hz.

The minor triad is classically given as 10:12:15, but around here the
consensus has been that 16:19:24 is also a perfectly functional
"minor" triad.

My question to you is, does a minor third in isolation sound any more
"minor" than a "major" third *in isolation*? If so, is it simply
because you're familiar with their context in diatonic scale, or is
there a fundamental difference in the way the intervals sound? Might
someone from another planet hear the minor third as sounding 'sweeter'
and 'happier'?

The way I hear it, it's more a product of the diatonic scale/culture
than of the way the intervals sound. Nevertheless, I have proposed
that harmonies which have low roughness and low "rootedness" might
sound intrinsically "minor". So 4:5:6 fits nicely into a harmonic
series, and its lowest tone corresponds to its strongest "virtual
fundamental". The same is not true of 10:12:15. The argument applies
also to the respective isolated thirds. 16:19:24, however, seems to
have stronger rootedness than 10:12:15. Does it sound less "minor"?

-Carl

From: "Carl Lumma" <ekin@lumma.org>

> The way I hear it, it's more a product of the diatonic scale/culture
> than of the way the intervals sound. Nevertheless, I have proposed
> that harmonies which have low roughness and low "rootedness" might
> sound intrinsically "minor". So 4:5:6 fits nicely into a harmonic
> series, and its lowest tone corresponds to its strongest "virtual
> fundamental". The same is not true of 10:12:15. The argument applies
> also to the respective isolated thirds. 16:19:24, however, seems to
> have stronger rootedness than 10:12:15. Does it sound less "minor"?

I interpret minor chords as being based on a common *overtone* as opposed to
undertone/fundamental. D minor can be expressed as 1/6:1/5:1/4 (and the
natural minor sixth, third inversion, adds 1/7), if 1/1 is an A.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> The minor triad is classically given as 10:12:15, but around here the
> consensus has been that 16:19:24 is also a perfectly functional
> "minor" triad.

What about 6:7:9?

>> The minor triad is classically given as 10:12:15, but around here the
>> consensus has been that 16:19:24 is also a perfectly functional
>> "minor" triad.
>
>What about 6:7:9?

Perfectly valid, though some feel it sounds out of place in common-
practice music, and for those folks whatever part of "minor" is
defined by common-practice music wouldn't apply to 6:7:9.

-Carl

>> The way I hear it, it's more a product of the diatonic scale/culture
>> than of the way the intervals sound. Nevertheless, I have proposed
>> that harmonies which have low roughness and low "rootedness" might
>> sound intrinsically "minor". So 4:5:6 fits nicely into a harmonic
>> series, and its lowest tone corresponds to its strongest "virtual
>> fundamental". The same is not true of 10:12:15. The argument applies
>> also to the respective isolated thirds. 16:19:24, however, seems to
>> have stronger rootedness than 10:12:15. Does it sound less "minor"?
>
>I interpret minor chords as being based on a common *overtone* as opposed
>to undertone/fundamental. D minor can be expressed as 1/6:1/5:1/4 (and
>the natural minor sixth, third inversion, adds 1/7), if 1/1 is an A.

That's Partch's theory, but 16:19:24 throws an exception, if you think
it sounds minor.

-Carl

>My question to you is, does a minor third in isolation sound any more
>"minor" than a "major" third *in isolation*? If so, is it simply
>because you're familiar with their context in diatonic scale, or is
>there a fundamental difference in the way the intervals sound? Might
>someone from another planet hear the minor third as sounding 'sweeter'
>and 'happier'?

Here's an interesting approach to studying this, for the consonance/
dissonance question....

http://tinyurl.com/e3e1

-Carl